In The World Is Flat, Thomas L. Friedman doesn't precisely claim that India is "flattening the world," but rather that many features of business in India are examples of how the world is becoming flatter.
The term "flattening" is one Friedman uses to indicate removing barriers to globalization. He suggests that the first stage in this was the beginning of global exploration, when Europeans started to visit other continents and global trade became increasingly significant. The British colonization and domination of India led to extensive trade and thus could be considered part of this as it led to increasing the movement of goods and people between the two countries.
The twenty-first century marks the beginning of global competition and global supply chains, facilitated by advances in computing and communications, allowing seamless integration across vast geographical areas. India and China have been especially important in this, with India serving as a back end to data processing and call centers for many firms located in the US and Europe. Rather than industries competing locally, they now compete globally.
Thus Friedman takes as a striking image of this flattening a wall screen in India's Infosys Technologies Limited offices and talks about how their global supply chain is support by the ability to be virtually present anywhere in the world via video conferencing.